Enumeration of Cubic Cayley Graphs on Dihedral Groups  

作　　者：Xue Yi HUANG Qiong Xiang HUANG Lu LU 

机构地区：[1]College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2017年第7期996-1010,共15页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11671344 and 11531011)

摘　　要：Let p be an odd prime, and D2p = （a,b I aP = b2 = l,bab= a 1） the dihedral group of order 2p. In this paper, we completely classify the cubic Cayley graphs on D2p up to isomorphism by means of spectral method. By the way, we show that two cubic Cayley graphs on D2p are isomorphic if and only if they are cospectral. Moreover, we obtain the number of isomorphic classes of cubic Cayley graphs on D2 by using Gauss＇ celebrated law of quadratic reciprocity.Let p be an odd prime, and D2p = （a,b I aP = b2 = l,bab= a 1） the dihedral group of order 2p. In this paper, we completely classify the cubic Cayley graphs on D2p up to isomorphism by means of spectral method. By the way, we show that two cubic Cayley graphs on D2p are isomorphic if and only if they are cospectral. Moreover, we obtain the number of isomorphic classes of cubic Cayley graphs on D2 by using Gauss＇ celebrated law of quadratic reciprocity.

关 键 词：Cayley graph dihedral group cospectral isomorphic classes quadratic reciprocity 

分 类 号：O152[理学—数学]